Estimators for the difference in means/medians of related samples and their properties and assumptions.
Cohen's d is the most popular estimator using the difference between the means divided by the pooled sample standard deviation. Cohen's d is a biased estimator of the population standardized mean difference (although the bias is very small and disappears for moderate to large samples) whereas Hedge's g applies an unbiasing constant to correct for the bias.
A shift in location is equivalent to a difference between means/medians when the distribution of the differences is symmetric. Symmetry is quite often inherently satisfied for paired data.
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